Spatially Aware Cell Cluster (SPACCL) Graphs

1. A non-transitory, computer-readable storage medium storing computer-executable instructions that when executed by the computer control the computer to perform a method for predicting a risk of disease by examining architectural features of stromal and epithelial tissue with a spatially aware cell cluster graph (SpACCl), comprising: accessing an image of a region of pathological tissue; identifying a stromal compartment in the image; identifying an epithelial compartment in the image, where the epithelial compartment is distinguishable from the stromal compartment; identifying a plurality of cluster nodes in the image, where a cluster node comprises a plurality of nuclei, and where identifying a plurality of cluster nodes comprises: identifying a stromal cluster node in the stromal compartment, and identifying an epithelial cluster node in the epithelial compartment; constructing electronic data associated with a spatially aware stromal sub-graph G S by connecting a first stromal cluster node with a second, different stromal cluster node, where the probability that the first stromal cluster node is connected with the second stromal cluster node is based, at least in part, on a probabilistic decaying function of the relative distance between the first stromal cluster node and the second stromal cluster node; constructing a spatially aware epithelial sub-graph G E by connecting a first epithelial cluster node with a second, different epithelial cluster node, where the probability that the first epithelial cluster node is connected with the second epithelial cluster node is based, at least in part, on a probabilistic decaying function of the relative distance between the first epithelial cluster node and the second epithelial cluster node; extracting local graph features from the sub-graphs G S and G E ; and predicting the risk of disease, based, at least in part, on the local graph features.

2. The non-transitory, computer-readable storage medium of claim 1 , where identifying a stromal compartment in the image and identifying an epithelial compartment in the image comprises: partitioning the image into a plurality of spatially coherent super-pixels; identifying nuclei within a super-pixel; generating a set of measurements by measuring the intensity and texture of the super-pixel and a neighboring super-pixel; training a classifier on the set of measurements; using the classifier to classify the super-pixel as either a stromal super-pixel or epithelial super-pixel; upon determining that the super-pixel is a stromal super-pixel, assigning the stromal super-pixel to the stromal compartment; and upon determining that the super-pixel is an epithelial super-pixel, assigning the epithelial super-pixel to the epithelial compartment.

3. The non-transitory, computer-readable storage medium of claim 2 , where the classifier is a Support Vector Machine (SVM) classifier, and where the SVM classifier is trained on the set of measurements using hand-labelled super-pixels.

4. The non-transitory, computer-readable storage medium of claim 1 , where identifying a plurality of cluster nodes in the image comprises: sampling three consecutive points (c w−1 , c w , c w+1 ) on a contour; computing an angle θ(c w ) between a plurality of vectors, where the plurality of vectors is defined by sampling the three consecutive points on the contour; determining a degree of concavity, where the degree of concavity is proportional to the angle θ(c w ); designating a point as a concavity point if θ(c w )>θ t , where θ t is an empirically set threshold degree; calculating a number of concavity points, and upon determining that the number of concavity points c w ≧1, classifying the contour as a cluster node.

7. The non-transitory, computer-readable storage medium of claim 6 , where a set of edges E i in the sub-graph G S or the sub-graph G E is defined as E i ={(u, v): r<d(u, v) −α , ∀u, vεV i }, where r is a real number between 0 and 1, and where α controls the density of the sub-graph.

8. The non-transitory, computer-readable storage medium of claim 7 , where extracting local graph features from the sub-graph G S and the sub-graph G E comprises extracting a clustering coefficient C, a clustering coefficient D, a giant connected component, an average eccentricity, a percent of isolated points, a number of central points, or a skewness of edge lengths.

9. The non-transitory, computer readable storage medium of claim 8 , where the clustering coefficient C describes a ratio of a total number of edges among neighbors of a cluster node to a total maximum possible number of edges among neighbors of the cluster node, per cluster node, where the clustering coefficient C is defined as: C ~ = ∑ u = 1  V  ⁢ C u  V  , where ⁢ ⁢ C u =  E u  ( k u 2 ) = 2 ⁢  E u  k u ⁡ ( k u - 1 ) .

10. The non-transitory, computer readable storage medium of claim 8 , where the clustering coefficient D describes a ratio of a total number of edges among neighbors of a cluster node and the cluster node itself to a total maximum possible number of edges among neighbors of the cluster node and the cluster node itself, per cluster node, where the clustering coefficient D is defined as D ~ = ∑ u = 1  V  ⁢ D u  V  , where ⁢ ⁢ D u = k u +  E u  ( k u + 1 2 ) = 2 ⁢ ( k u +  E u  ) k u ⁡ ( k u + 1 ) .

11. The non-transitory, computer-readable storage medium of claim 8 , where the giant connected component describes a ratio between a number of cluster nodes in a largest connected component in the sub-graph and the total number of cluster nodes in the sub-graph.

12. The non-transitory, computer-readable storage medium of claim 8 , where average eccentricity is defined as ∑ u = 1  V  ⁢ ε u  V  , where eccentricity of a u th cluster node ε u , u=1·|V|, is the maximum value of the shortest path length from cluster node u to any other cluster node on the sub-graph.

13. The non-transitory, computer-readable storage medium of claim 8 , where the percent of isolated points describes the percentage of isolated cluster nodes in the sub-graph, where an isolated cluster node has a degree of 0.

14. The non-transitory, computer-readable storage medium of claim 8 , where the number of central points describes the number of cluster nodes within the sub-graph that have an eccentricity equal to the sub-graph radius.

15. The non-transitory, computer-readable storage medium of claim 8 , where the skewness of edge lengths describes the edge length distribution in the sub-graph.

16. An apparatus for predicting disease aggressiveness using a spatially aware cell cluster graph, comprising: a processor; a memory; an input/output interface; a set of logics; and an interface to connect the processor, the memory, the input/output interface and the set of logics, the set of logics comprising: an image acquisition logic that acquires an image of a region of tissue; a compartment classification logic that partitions the image into a stromal compartment and an epithelial compartment; a cluster node identification logic that identifies a cluster of nuclei as a cluster node; a sub-graph construction logic that constructs a stromal sub-graph G S and an epithelial sub-graph G E where the sub-graph construction logic constructs the stromal sub-graph G S by linking a first stromal cluster node and a second, different stromal cluster node, where the probability that the first stromal cluster node will be linked to the second stromal cluster node is based, at least in part, on a probabilistic decaying function of the distance between the first stromal cluster node and the second stromal cluster node, and where the sub-graph construction logic constructs the epithelial sub-graph G E by linking a first epithelial cluster node and a second, different epithelial cluster node, where the probability that the first epithelial cluster node will be linked to the second epithelial cluster node is based, at least in part, on a probabilistic decaying function of the distance between the first epithelial cluster node and the second epithelial cluster node; a feature extraction logic that extracts global features and local features from the stromal sub-graph G S and the epithelial sub-graph G E ; and a disease aggressiveness prediction logic that produces electronic data that predicts the aggressiveness of a disease in the region of tissue, based, at least in part, on the global features and local features.

17. The apparatus of claim 16 , where the compartment classification logic partitions the image into a set of super-pixels, identifies nuclei within a super-pixel, generates a set of measurements by measuring the intensity and texture of the super-pixel and neighboring super-pixels, and classifies the super-pixel as being a stromal super-pixel or an epithelial super-pixel by training a Support Vector Machine (SVM) classifier on the set of measurements with hand-labelled super-pixels from a plurality of images, where a stromal-compartment comprises at least one stromal super-pixel, and an epithelial compartment comprises at least one epithelial super-pixel.

18. The apparatus of claim 16 , where the cluster node identification logic: samples three consecutive points (c w−1 , c w , c w+1 ) on a contour that encloses the cluster of nuclei, computes an angle θ(c w ) between a plurality of vectors, where the plurality of vectors is defined by sampling the three consecutive points on the contour, determines a degree of concavity, where the degree of concavity is proportional to the angle θ(c w ), designates a point as a concavity point if θ(c w )>θ t , where θ t is an empirically set threshold degree, calculates the number of concavity points, and upon determining that the number of concavity points c w ≧1, and classifies the contour as a cluster node, where a cluster node in the epithelial compartment is an epithelial cluster node, and where a cluster node in the stromal compartment is a stromal cluster node.

19. An apparatus comprising: a processor; a memory; an input/output interface; a set of logics; and an interface to connect the processor, the memory, the input/output interface and the set of logics, the set of logics comprising: a first logic that acquires an image of a region of interest; a second logic that partitions the image into at least a first compartment and a second compartment, where the second compartment is distinguishable from the first compartment; a third logic that identifies cluster nodes, where a cluster node identified in the first compartment is a first compartment cluster node, and a cluster node identified in the second compartment is a second compartment cluster node; a fourth logic that generates a first compartment sub-graph G 1 and a second compartment sub-graph G 2 , where a sub-graph is generated by connecting a first cluster node in a compartment with a second, different cluster node in the same compartment, where the probability the first cluster node will be connected to the second cluster node is based on a probabilistic decaying function of the Euclidean distance between the first cluster node and the second cluster node, where the density of the sub-graph is controllable, and a fifth logic that extracts global metrics and local metrics from the sub-graphs G 1 and G 2 and controls an automated diagnostic system to classify the image, based, at least in part, on the global metrics and local metrics.